[Claude Marché told me this puzzle. At first, it seems quite similar to "Catching a spy" (below), but the solution is entirely unrelated.]
There are five holes arranged in a line. A hermit hides in one of them. Each night, the hermit moves to a different hole, either the neighboring hole on the left or the neighboring hole on the right. Once a day, you get to inspect one hole of your choice. How do you make sure you eventually find the hermit?